| To use computational methods to study the kinetics of combustion reaction of either alkanes or biofuels, two great challenge issues need to be addressed. The first one is the multi-structure effect, which makes the reactive potential energy surface complex, and requires considering multiple stationary states and multiple reaction paths to calculate the thermal rate. The second issue oringinates from torsional anharmonicity, which causes the harmonic oscillator approximation and normal mode analysis to fail and requires treating the torsions using different models in different temperature regimes. To treat the multi-structural and torsional anharmonicity correctly, we developed the internal-coordinate multi-structural approximation to calculate the partition functions for large molecules. This new method can predict more accurate partition functions for complex molecules in both the low and high temperature ranges. We also developed two new formulations of variational transtition state theory (VTST): multi-structure and multi-path VTST with multi-dimensional tunneling to calculate the thermal rates of hydrogen-transfer reactions in a broad temperature range. These formulations include both multi-structure and torsional anharmonicity effects and a more accurate means to evaluate vairational and tunneling effects using multiple reaction paths in the calculation. The thesis work is presented as four chapters, as follows:;Chapter one discusses the theory of the internal-coordinate multi-structural approximation, also called the multi-structure torsional (MS-T) approximation and its application to various molecules. Although this work was mainly contributed by J. Zheng and S. Mielke in our group, the author still would like to present this part in the thesis because this part is one of the fundamentals for the following chapters.;Chapter two investigates the thermodynamics properties of two complex molecules, n-hepane and isoheptane, using the MS-T method. The results were compared with experimental data from the API Tables and TRC data sets and with the empirical group additivity method, to further demonstrate the success of the MS-T approximation in calculating the partition functions of large molecules.;Chapter three focuses on presenting multi-structure variational transion state theory (MS-VTST) with torsional anhormicity, which includes both multi-structure and torsional anharmonicity effects for reactants, products, and transition states, but uses only the reaction path with the lowest vibrationally adiabatic ground-state potential energy barrier to calculate the variational and tunneling effects. To apply this theory, we studied the thermal rate of the 1,4-hydrogen shift reaction of 1-pentyl radical, and by comparing with experimental data, demonstrated that the MS-VTST rate is more accurate than that obtained by conventional single-structure VTST (SS-VTST).;The last chapter, chapter four, extends the MS-VTST method to multi-path VTST (MP-VTST), which includes not only the multi-structure effect, but also the contribution of the variational and tunneling effects of all reaction paths. We applied this formulation to calculate the thermal rate of 1,4-hydrogen shift isomerization of the 2-cyclohexylethyl radical using two reaction paths. |
